کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5778123 1633426 2017 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The strength of infinitary Ramseyan principles can be accessed by their densities
ترجمه فارسی عنوان
قدرت اصول رامسیان بی نهایت را می توان با تراکم آنها مقایسه کرد
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
چکیده انگلیسی
In this article, we conduct a model-theoretic investigation of three infinitary Ramseyan statements: the Infinite Ramsey Theorem for pairs and two colours (RT22), the Canonical Ramsey Theorem for pairs (CRT2) and the Regressive Ramsey Theorem for pairs (RegRT2). We approximate the logical strength of these principles by the strength of their first-order iterated versions, known as density principles. We then investigate their logical strength using strong initial segments of models of Peano Arithmetic, in the spirit of the classical article by Paris and Kirby, hereby re-proving old results model-theoretically. The article is concluded by a discussion of two further outreaches of densities. One is a further investigation of the strength of the Ramsey Theorem for pairs. The other deals with the asymptotics of the standard Ramsey function R22.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 168, Issue 9, September 2017, Pages 1700-1709
نویسندگان
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